Pricing related to second-best problems

3.7.1. Pricing under a budget constraint

Une problem that has been analyzed extensively is the fact that strict marginal cost pricing does not guarantee revenues which will secure the financial survival of operations characterized by decreasing cost. P: ;<nng based on SRMC or LRMC do not guarantee that total costs will be covered.

Boiteux (1952, pp. 125-126 and 1956) was clearly aware of the fact that this would occur only by chance.

A financial deficit must be covered in one way or another. In a first-best solution this can be done by lump-sum transfers from the government.

However, if sufficient lump-sum taxes are not available, this alternative is impossible by definition. Public funds could be raised to cover the deficit, although not without costs; see Vickery (1963).

If subsidies from public funds are ruled out, a break-even constraint has to be placed on the public utility. That is, the utility has to raise sufficient revenues through its tariff to cover all the costs of operation. This can be accomplished either by letting linear prices deviate from marginal cost or by adopting some kind of nonlinear pricing schedule such as two-or multi-part tariffs two-or block tariffs. The optimal pricing scheme, of course, is the one that fulfills the constraint while distorting resource allocation as little as possible.

Boiteux analyzed the problem of finding optimal linear prices under a budget constraint. In fact, Tresch (1981) called this "the Boiteux Prob-lem", although it is closely related to the problem of optimal taxation, as pointed out by Baumol and Bradford (1970).

Boiteux and several others analyzed this problem by using a general equilibrium model with many individuals, goods and factors; see Rees (1968), Turvey (1971), Hagen (1979) andTresch (1981). The government was assumed to be able tc redistribute income in a nondistortive way so as to satisfy equity ambitions. This means that distributional considera-tions could be omitted and the analysis could be focused on the allocation problem of finding prices for public outputs that will maximize social welfare, given the break-even or budget constraint. The pricing rule derived in this way has been called Ramsay pricing or the inverse elasticity ru'e; see Ramsay (1927). Given the revenue requirement, prices will dit* tr from marginal costs to a larger extent for goods that are characterized '»y low demand (own price) and/or supply elasticities than

for goods with more elastic (compensated) demand or supply; see also the discussion in Baumol-Bradford (1970).

One particular feature of this approach is that the reason for relying on second-best pricing is obscure when the government is assumed to have access to lump-sum taxes to redistribute income, at least if the rest of the economy is assumed to be perfectly competitive. Under such cir-cumstances it is, of course, preferable from an efficiency point of view to choose the first-best solution by using lump-sum subsidies from public funds. In order for Ramsay pricing to be of real interest as a solution of the Boiteux problem, such lump-sum transfers should not be assumed.

Carlin (1974) tackled this pricing problem and Bös (1983) presented an analysis in an extended Boiteux model without assuming lump-sum taxes. The way in which optimal linear prices will deviate from marginal cost in this model depend on the price sensitivity of the ordinary Mar-shallian demand and on distributional objectives.

Instead of relying solely on Ramsay pricing to meet a given budget constraint, it might be preferable to adopt some kind of nonlinear pricing.

In practice block tariffs as well as two- and multi-part tariffs have been used extensively in rate-setting, even if the welfare implications of these tariffs have not been given due considerations. However, the theoretical aspects of using two-part tariffs in particular have received more atten-tion; see Oi (1971), Ng and Weisser (1974), Leland and Meyer (1976), Bohm (1977), Spence (1977), Willig (1978), Auerback and Pellechio (1978), Mitchell (1978), Brown and Heal (1980), Ordover and Panzar (1980) and Berg (1983). In addition to a charge per unit consumed, a two-part tariff includes a component which is independent of the volume consumed. Ideally, the fixed charge should not exceed the consumer's surplus at a per-unit price equal to the SRMC for any potential consumer, in which case the tariff will secure a first-bets solution. If this is not feasible, a combination of a linear price and a two-part tariff, with an option for the consumer to choose how his own consumption should be billed, can be preferable to either pricing scheme in isolation.

The determination of the budget constraint is often rather arbitrary, geographically as well as temporally. First of all, the size of the geographical area to be encompassed by a budget constraint is not self-evident. Should it cover a particular transmission line, a whole collective network, a region or the entire country? In general, the larger the area covered by a budget constraint, the fewer the restrictions in regard to achieving efficient utilization of existing capacity. Second, it is not obvious whether a budget constraint should be applied for, e.g., one fiscal year at a time or a considerably longer budgetary period. In this case as well, the possibilities of achieving efficient capacity utilization

increase if the budget constraint is defined over a longer period; see Bohman (1983 ch. 4). Third, the budget constraint is affected by the choice of required rate of return, repayment period, depreciation prin-ciples, etc. Narrowly formulated budget constraints in a geographical and temporal sense reduce the possibilities of achieving efficient utiliza-tion prices, and vice versa.

3.7.2 Other second-best problems

It is debatable whether considerations of a budget constraint for a public utility should be regarded as a second-best problem or not. In addition to the terminology issue, there are other reasons why second-best solu-tions have to be chosen with respect to pricing and investment decisions in the public sector:

• Market imperfections, e.g., monopolistic conditions en the market for substitutes or complements to the commodity in question or the existence of distortive taxation;

• Limited possibilities of achieving income distribution by means of general instruments.

The Boiteux model presented above is also well suited for taking market imperfections into account. If such imperfections cannot be eliminated, a piecemeal policy based on marginal cost pricing may be quite mislead-ing from an efficiency point of view. Instead, there are efficiency reasons for letting prices for public outputs deviate from marginal costs. How they should deviate depends on whether public outputs are complements or substitutes to the price-distorted commodities; see Hagen (1979) and Bös (1983).

So far the objective of public utility pricing has been formulated to achieve efficient utilization in the production and distribution of public utilities. Another objective or constraint on the efficiency maximization problem appears if income distribution effects have to be taken into account; see Feldstein (1971), Spence (1977), Aurbach and Pellechio (1978), and Bös (1983). However, such considerations complicate and limit the possibilities of reaching a price or tariff aimed at efficiency.

First, it may be difficult to design a sufficiently simple tariff based on such considerations. Second, there are coordination problems; for ex-ample, will some public utility repeat what some other public utility (or the government) has already considered in its tariff? The problems of designing a clear and simple tariff and decentralizing the responsibility for more than one objective should be tackled prior to determining whether income distribution should be regarded as an objective in designing electricity tariffs.

3.8. Conclusions

The way in which electricity tariffs are designed is important with respect to

a) How the at each instant existing production and distribution system is used

b) The financial outcome for suppliers, and to a smaller degree to c) The distribution of real incomes in society.

The technology of electricity production and distribution is characterized by important indivisibilities, ex ante as well as ex post. The ex ante indivisibilities lead to that capacity can only (economically) be changed in a stepwise non-marginal way. Economic theory tells us that when capacity is lumpy in this way adherence to pricing according to SRMC is a means to achieve an optimal use of existing capacity. Such a pricing is also compatible with an optimal timing and dimensioning of new capacity into the system. SRMC pricing thus leads to an optimal solution of a).

The ex post indivisibilities in a system consisting of different kinds of plants with different variable cost levels lead to variations in the SRMC as a consequence of variations in demand over time. Efficient use of existing capacity calls for a peak load pricing scheme to cope with demand variations over day/night and seasons.

The existence of indivisibilities makes it efficient to concentrate produc-tion to a limited number of places. Consumpproduc-tion is usually more dis-persed. To overcome distances transmission lines are used, which in themselves also represent an indivisibility. As there are costs associated with the use of such a transmission line, in the form of energy losses, and as these costs depend on transmission direction and distance, energy prices should also be differentiated over space.

Both demand and supply arc subject to stochastic changes. Instan-taneous non-foreseeable changes in such conditions cannot generally be translated into price signals to achieve equilibrium. When such changes occur, rationing in one way or another may be the only way out. This may also be true for changes foreseeable only at short notice. But, specially designed tariffs can be a supplementary means to cope with such situations. However, many types of stochastic variations, i.e. cycli-cal and precipitating variations, can with reasonable accuracy be foreseeable early enough to permit price changes to be announced well

in advance and thus giving consumers a reasonable time to reconsider and adjust consumption plans. So SRMC-pricing is still an important means to achieve an optimal solution of a) even when uncertainty is taken into account.

In the literature of electricity pricing stable prices have often been said to be a prerequisite for efficient investment strategies by the consumers.

Even if this is an empirical question we have on theoretical grounds challenged the validity of this preposition. It is not stable prices but a stable pricing principle that leads to efficiency.

Pricing based on SRMC will normally not lead to an acceptable solution to b). In a fully adjusted long-run equilibrium optimal prices can either exceed or fall short of average costs. In many short-run equilibria the optimal prices will not generate enough revenue to cover the total costs of the system. If subsidies from public funds are not feasible, it is then necessary to design tariffs considering a budget constraint. If linear prices are chosen and distributional aspects are disregarded, our solu-tion is to let prices deviate from SRMC according to the inverse elasticity rule. Another solution can be to use some non-linear pricing choice such as two- or multipart tariffs. In many cases a combination of linear prices and a two-part tariff is preferable to get an acceptable solution of b) with the least possible deadweight loss in terms of a).

Another feature that can be a rationale for deviating from SRMC-pricing is when there are important market imperfections in related markets.

If such imperfections cannot be dealt with directly, an indirect way to tackle them can be to adjust electricity prices. Depending on whether the goods in these related markets are complements OT substitutes to electricity and the type of imperfection in question second best electricity prices can either exceed or fall short of SRMC in order to solve a) in an optimal way. In cases where it would be second best optimal to set energy prices below SRMC, such a pricing policy may be difficult to combine with an acceptable solution of b).

A tariff that sustains an optimal allocation in terms of a) and fulfills a restriction in terms of b) may of course also be resented from a distribu-tional point of view. In such a case, it might be in order to choose another tariff design with more acceptable distributional characteristics. How-ever, to use electricity tariffs in order to improve the income distribution can be difficult as well as expensive in terms of dead-weight losses. Many problems concerning choice of distributional means, simplicity in tariffs and decentralization of more than one objective should be tackled prior to making income distribution to a decisive feature when designing electricity tariffs.

Chapter 4.